解(1) a²-9b²=a²-(3b)²=(a+3b)(a-3b)解(2) -16m²+(m-n)²=(m-n)²-16m²=(m-n)²-(4m)²=[(m-n)+4m][(m-n)-4m]=(5m-n)(-3m-n)=-(5m-n)(3m+n)解(3) (x-2y)²-4(2x-y)²=(x-2y)²-[2(2x-y)]²=[(x-2y)+2(2x-y)][(x-2y)-2(2x-y)]=(x-2y+4x-2y)(x-2y-4x+2y)=-3x(5x-4y)解(4) a²(x-y)-b²(x-y)=(x-y)(a²-b²)=(x-y)(a+b)(a-b)解(5) 16m^4-n^4 ^表示乘方=(4m²)-(n²)²=(4m²+n²)(4m²-n²)=(4m²+n²)(2m+n)(2m-n)解(6) (a+b+c+d)²-(a-b+c-d)²=[(a+b+c+d)+(a-b+c-d)][(a+b+c+d)-(a-b+c-d)]=(a+b+c+d+a-b+c-d)(a+b+c+d-a+b-c+d)=(2a+2c(2b+2d)=4(a+c)(b+d)
解(1) a²-9b²=a²-(3b)²=(a+3b)(a-3b)解(2) -16m²+(m-n)²=(m-n)²-16m²=(m-n)²-(4m)²=[(m-n)+4m][(m-n)-4m]=(5m-n)(-3m-n)=-(5m-n)(3m+n)解(3) (x-2y)²-4(2x-y)²=(x-2y)²-[2(2x-y)]²=[(x-2y)+2(2x-y)][(x-2y)-2(2x-y)]=(x-2y+4x-2y)(x-2y-4x+2y)=-3x(5x-4y)解(4) a²(x-y)-b²(x-y)=(x-y)(a²-b²)=(x-y)(a+b)(a-b)解(5) 16m^4-n^4 ^表示乘方=(4m²)-(n²)²=(4m²+n²)(4m²-n²)=(4m²+n²)(2m+n)(2m-n)解(6) (a+b+c+d)²-(a-b+c-d)²=[(a+b+c+d)+(a-b+c-d)][(a+b+c+d)-(a-b+c-d)]=(a+b+c+d+a-b+c-d)(a+b+c+d-a+b-c+d)=(2a+2c(2b+2d)=4(a+c)(b+d)